Reciprocal lattice

Dr_Pill

I got a bunch of questions about reciprocal lattice, I start with this one:

In an x-ray experiment:

For one specific orientation of your incident beam on your real lattice, only a portion of the points of your reciprocal lattice will become visible as your diffraction pattern right?

See my picture



For one incident beam, only the parallel planes are involved in your diffraction and so only the reciprocal lattice points that represent these set of parallel planes will becoem visible on your diffraction pattern

If you want to make other reciprocal points points visible on your diffraction pattern, u have to change the orientation of your incident beam so that another set of parallel planes is involved in diffraction



So in first picture, your blue beam will get the reciprocal points that representing the green parallel planes visible on your diffraction pattern.

Second picture, the same blue beam does nothing on the purple planes, so the reciprocal points that represents the purple planes will not be visible on the diffraction pattern.

Is this correct?

ZapperZ

It might help with the Forum formatting if you reduce the size of your image to no more than 800 pixels by 600 pixels. There's no reason for it to be THIS big.

Zz.

Dr_Pill

Ok, like this? But now my picture is unsharp.

ZapperZ

Remove the image, and upload a new, resized version.

Zz.

M Quack

Dr. Pill,

your images are in real space, not reciprocal space.

It is perfectly possible to align a single crystal such that two or even three sets of lattice planes fulfull the Bragg condition simultaneously.

For the two-beam case this can be done by aligning one Bragg peak (corresponding to the reciprocal space vector Q), and by then rotating the crystal about the vector Q until you excite a second reflection (=changing the azimuthal angle). To get 3 simultaneous reflections you also need to tune the photon energy just right.

The effect is known by several names including "Umweganregung", "Renninger effect" and "Multiple beam diffracton". It was first described in 1935.

The following links give a bit more informaiton:

P. P. Ewald, Rev. Mod. Phys. v37, pp46 (1965)
http://rmp.aps.org/abstract/RMP/v37/i1/p46_1
This is an excellent review article about the early theory of x-ray diffraction, written by one of the founding fathers. Highly recommended if you are interested in x-rays.

Renninger, Z. Phys v. 106 pp 141 (1937) in German
http://link.springer.com/article/10.1007%2FBF01340315

Description of a computer code for calculating Umwegs.
http://www1.uni-hamburg.de/mpi/rossm...Z_Krist_85.pdf